The long-awaited report into the Bloody Sunday massacre will conclude that a number of the fatal shootings of civilians by British soldiers were unlawful killings, the Guardian has learned.

Lord Saville's 12-year inquiry into the deaths, the longest public inquiry in British legal history, will conclude with a report published next Tuesday, putting severe pressure on the Public Prosecution Service in Northern Ireland to prosecute soldiers.

Lord Trimble, the former leader of the Ulster Unionists and one of the architects of the Good Friday agreement, revealed to the Guardian that when Tony Blair agreed to the inquiry in 1998, he warned the then prime minister that any conclusion that departed "one millimetre" from the earlier 1972 Widgery report into the killings would lead to "soldiers in the dock".

One unionist MP who did not wish to be named described the conclusion of unlawful killings as a "hand-grenade with the pin pulled out that is about to be tossed into the lap of the PPS" in Northern Ireland.

Thirteen unarmed civilians, all of them male, were shot dead at a civil rights march in the Bogside area of Derry in January 1972. A 14th man died of his wounds several months later.

The killings electrified nationalist protests against British rule in Northern Ireland and Bloody Sunday became a critical moment in the history of the Troubles, dramatically boosting the popularity of the Provisional IRA in the province and, according to many people, acting as a catalyst for much of the violence that followed.

The results of Saville's hearing will be released to the public at 3.30pm on Tuesday when David Cameron announces its publication to the House of Commons.

Up to 10,000 people are expected to march around lunchtime that day into Guildhall Square in Derry, where they will watch live reports about the inquiry's conclusions on giant television screens. They will trace the same route that the civil rights marchers had attempted to take on Bloody Sunday, which the Stormont government, dominated in 1972 by unionists, had banned.

Families of those killed in the massacre 38 years ago have focused on a number of soldiers who were identified and gave evidence during the 12 year old tribunal. These include "Soldier F" who, according to the relatives of the Bloody Sunday dead, shot four to six of the victims. Told during the inquiry that his evidence amounted to perjury, he did not demur.

Though witnesses were protected from self-incrimination, an exception was made for perjury. And government law officers made it clear that criminal prosecution against an individual was not ruled out in the light of any evidence that emerged from other witnesses or from documents. Sources familiar with the inquiry said yesterday that Saville may not explicitly recommend criminal prosecutions and much will depend on his message, whether direct or indirect, to the PPS.

The PPS, headed by Sir Alasdair Fraser, will make the decision on prosecutions because the killings occurred in its jurisdiction, rather than the Crown Prosecution Service in London. Fraser will have to take into account the public interest in a prosecution, and the likelihood of securing a conviction.

Among survivors who were shot on the day and the families of the dead, there are many demanding that a number of British paratroopers should be prosecuted through the courts.

They could initiate a private prosecution and sue for compensation in a civil court.

Trimble, a Nobel peace prize winner, said that during the all-party talks of late 1997 and early 1998 he told Blair that a new inquiry would end up with soldiers being dragged through the courts.

He described the establishment of the tribunal during the peace talks as a "sideline deal independent from the Belfast agreement".

On his warning to Blair, Trimble said: "I just reminded him that the Widgery report of 1972 concluded that the troops' behaviour, to quote from the report, 'bordered on the reckless'.

"Then I told the prime minister that if you moved from one millimetre from the that conclusion you were into the area of manslaughter, if not murder," he said.

"I pointed out to Blair that we would see soldiers in the dock. I told him that at the time of the talks leading to the Belfast agreement," Trimble said.

Blair and the then Northern Ireland secretary, Mo Mowlam, announced the establishment of the Saville inquiry on 30 January 1998 – the 26th anniversary of the shootings, citing "compelling new evidence".

At the time Blair and Mowlam, who has since died, were locked in the intensive negotiations between unionists and nationalist that ultimately led to the Good Friday agreement of 1998.

However, Trimble said that the inquiry was "not in any way part of the agreement".

He added: "At the time of the talks the parties, it seemed to me, did not want to be obsessing on the past. The problem was that Blair, for reasons that I can't understand, gave in to pressure for a selective inquiry."